A128853 - OEIS

%I #17 Oct 18 2020 14:34:19

%S 1,2,2,1,2,2,2,1,1,2,2,2,2,2,4,1,2,1,2,2,2,2,2,2,1,2,1,2,2,4,2,1,4,2,

%T 4,1,2,2,2,2,2,2,2,2,2,2,2,2,1,1,4,2,2,1,2,2,2,2,2,4,2,2,2,1,4,4,2,2,

%U 4,4,2,1,2,2,2,2,4,2,2,2,1,2,2,2,4,2,4,2,2,2,4,2,2,2,4,2,2,1,2,1,2,4,2,2,4

%N a(n) is the number of positive divisors of n which are coprime to phi(n) = A000010(n).

%H Antti Karttunen, <a href="/A128853/b128853.txt">Table of n, a(n) for n = 1..65537</a>

%e 12 is coprime to 4 positive integers (1,5,7 and 11) which are <= 12; so phi(12)=4. There are 2 divisors (1 and 3) of 12 that are coprime to 4. So a(12) = 2.

%p with(numtheory): a:=proc(n) local div,ct,j: div:=divisors(n): ct:=0: for j from 1 to tau(n) do if igcd(div[j],phi(n))=1 then ct:=ct+1 else fi od: ct; end: seq(a(n),n=1..140); # _Emeric Deutsch_, Apr 17 2007

%t Table[Total[Boole[CoprimeQ[Divisors[n],EulerPhi[n]]]],{n,120}] (* _Harvey P. Dale_, Oct 18 2020 *)

%o (PARI) A128853(n) = { my(ph=eulerphi(n)); sumdiv(n,d,(1==(gcd(d,ph)))); }; \\ _Antti Karttunen_, Sep 27 2018

%K nonn

%O 1,2

%A _Leroy Quet_, Apr 16 2007

%E More terms from _Emeric Deutsch_, Apr 17 2007